Electromagnetic curves and Rytov’s law in the optical fiber with Maxwellian evolution via alternative moving frame

Authors

  • Semra Nurkan Usak University
  • Hazal Ceyhan Ankara University
  • Zehra Özdemir Amasya University
  • İsmail Gök Ankara University

DOI:

https://doi.org/10.31349/RevMexFis.69.061301

Keywords:

Applications to physics, Magnetic flows, Vector fields, Ordinary differential equations, Electromagnetic theory, Maxwell’s equation

Abstract

In this study, we research the behavior of a linearly-polarized light wave in optical fiber and the rotation of the polarization plane through the alternative moving frame { N,C,W } in Minkowski 3-space. Then Berry’s phase equations are discussed for electromagnetic curves in the { C } and { W } directions along an optic fiber via alternative moving frame in Minkowski 3-space. Moreover, electromagnetic curve’s { C } and { W } Rytov parallel transportation laws are defined. Finally, we examine the electromagnetic curve’s Maxwellian evolution by Maxwell’s equation.

References

V. V. Vladimirski, Dokl. Akad. Nauk. SSSR 31 (1941) 222; reprinted in B. Markovski, S.I. Vinitsky (eds) Topological Phases in Quantum Theory, World Scientific, Singapore (1989).

Y. A. Kravtsov and Y. I. Orlov, Geometrical Optics of Inhomogeneous Media, (Springer-Verlag, Berlin, 1990).

E. M. Frins, W. Dultz, Rotation of the polarization plane in optical fibers, J. Lightwave Technol. 15 (1997) 144. https://doi.org/10.1109/50.552122

J .N. Ross, The rotation of the polarization in low briefrigence monomode optical fibres due to geometric effects, Opt. Quantum Electron. 16 (1984) 455. https://doi.org/10.1007/BF00619638

M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. Roy. Soc. London A. 392 (1984) 45. https://doi.org/10.1098/rspa.1984.0023

M. Kugler, S. Shtrikman, Berry’s phase, locally inertial frames, and classical analogues, Phys. Rev. D. 37 (1988) 934. https://doi.org/10.1103/physrevd.37.934

R. Dandoloff, Berry’s phase and Fermi–Walker parallel transport, Phys. Lett. A. 139 (1989) 19. https://doi.org/10.1016/0375-9601(89)90599-9

A. Comtet, On the Landau Hall levels on the hyperbolic plane, Ann. Phys. 173 (1987) 185. https://doi.org/10.1016/0003-4916(87)90098-4

M. Barros, A. Romero, J. L. Cabrerizo, M. Fernández, The Gauss-Landau-Hall problem on Riemanniansurfaces. J. Math. Phys. 46 (2005) 112905, https://doi.org/10.1063/1.2136215

M. Barros, J. L. Cabrerizo, M. Fernández, A. Romero, Magnetic vortex flament flows, J. Math. Phys. 48 (2007) 082904, https://doi.org/10.1063/1.2767535

T. Adachi, Kahler magnetic on a complex projective space, Proc. Jpn. Acad. Ser. A Math. Sci. 70 (1994) 12. https://doi.org/10.3792/pjaa.70.12

T. Adachi, Kahler magnetic flow for a manifold of constant holomorphic sectional curvature, Tokyo J. Math. 18 (1995) 473. https://doi.org/10.3836/tjm/1270043477

T. Körpınar, R.C. Demirkol, Electromagnetic curves of the linearly polarized light wave along an optical fiber in a 3D semi-Riemannian manifold. Journal of Modern Optics, 66 (2019) 857. https://doi.org/10.1080/09500340.2019.1579930

T. Sunada, Magnetic flows on a Riemann surface, In Proceedings of the KAIST Mathematics Workshop:Analysis and Geometry, Taejeon, Korea, 8 (1993) 93. https://cir.nii.ac.jp/crid/1574231873874473728

J. L Cabrerizo, M. Fernández and J. S. Gómez, The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A: Math. Theor. 42 (2009) 195201. https://doi.org/10.1088/1751-8113/42/19/195201

M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125 (1997) 1503. https://www.jstor.org/stable/2162098

Z. Bozkurt, ˙I. Gök, Y. Yaylı F. N. Ekmekci, A new approach for magnetic curves in 3D Riemannian manifolds, J. Math. Phys. 55 (2014) 053501. https://doi.org/10.1063/1.4870583

Z. Özdemir, A New Calculus for the Treatment of Rytov’s Law in the Optical Fiber, Optik 216 (2020) 164892, https://doi.org/10.1016/j.ijleo.2020.164892

H. Ceyhan, Z. Özdemir, ˙I. Gök, F. N. Ekmekci, Electromagnetic Curves and Rotation of the Polarization Plane through Alternative Moving Frame, European Physical Journal Plus 135 (2020) 1. https://doi.org/10.1140/epjp/s13360-020-00881-z

J.L. Cabrerizo, Magnetic fields in 2D and 3D sphere. J. Nonlinear Math. Phys. 20 (2013) 440 https://doi.org/10.1080/14029251.2013.855052

O. Bjorgum G. Thore, On Beltrami vector fields and flows, Part 1. Universitet I Bergen, Arbok (1951), Naturvitenskapelig rekke nr. 1.

A. W. Marris, Addendum to, Vector fields of solenoidal vectorline rotation, A class of permanent flows of solenoidal vectorline rotation. Arch. Rational Mech. Anal. 27 (1967) 195

N. E. Gurbuz, The pseudo-null geometric phase along optical fiber, Int. J. of Geometric Methods in Modern Phys. 18 (2021) https://doi.org/10.1142/S0219887821502303

T. Körpınar, R. C. Demirkol, Z. Körpinar, V. Asil, Maxwellian evolution equations along the uniform optical fiber in Minkowski space, Rev. Mex. Fis. 66 (2020) 431, https://doi.org/10.31349/revmexfis.66.431

F. Ates¸, E. Kocakus¸aklı, ˙I. Gök, F. N. Ekmekci, Tubular Surfaces Formed by Semi-spherical Indicatrices in E3 1, Mediterr. J. Math., 17 (2020) 127, https://doi.org/10.1007/s00009-020-01561-z

R. Betchov, On the curvature and torsion of an isolated vortex filament, Journal of Fluid Mechanics, 22 (1965) 471 https://doi.org/10.1017/S0022112065000915

L. S. Da Rios, Sul moto d’un liquido indefinito con un filetto vorticoso di forma qualunque, Rend, Circ. Matem. Palermo, 22 (1906) 117 https://doi.org/10.1007/BF03018608

W. K. Schief, Hidden integrability in ideal magnetohydrodynamics: The Pohlmeyer-Lund-Regge Model, Phys. of Plasmas, 10 (2003) 2677 https://doi.org/10.1063/1.1577347

W. K. Schief, C. Rogers, The Da Rios system under a geometric constraint: the Gilbarg problem, Jour. of Geometry and Physics, 54 (2005) 286 https://doi.org/10.1016/j.geomphys.2004.10.001

H. Hasimoto, A soliton on a vortex filament, Jour. of Fluid Mech., 51 (1972) 477 https://doi.org/10.1017/S0022112072002307

A. Mukhopadhyay, V. Vyas, P. Panigrahi, Rogue waves and breathers in Heisenberg spin chain, Eur. Phys. J. B 88 (2015) 188 https://doi.org/10.1140/epjb/e2015-60229-8

V. Banica, E. Miot, Evolution, interaction and collisions of vortex filaments, Differential Integral Equations, 26 (3/4) (2013) 355 https://doi.org/10.48550/arXiv.1202.2580

M. Grbovic, E. Nesovic, On Backlund transformation and vortex filament equation for pseudo-null curves in Minkowski 3- space, Int. J. Geom. Methods Mod. Phys. 13 (2016) 1650077 https://doi.org/10.1142/S0219887816500778

J. Amor, A. Gimenez, P. Lucas, Integrability aspects of the vortex filaments equation for pseudo-null curves, Int. J. Geom. Methods Mod. Phys. 14 (2017) 1750090, https://doi.org/10.1142/S0219887817500906

M. Hesami, M. Avazpour, M. M. Méndez Otero, J. J. A. Rodríguez, Evolution of rectangular and triangular initial beam profiles in positive Kerr local medium, Supl. Rev. Mex. Fis. 1 (2020) 13 https://doi.org/10.31349/SuplRevMexFis.1.13

M. Hesami, M. Avazpour, M. M. Méndez Otero, J. Arriaga, M. D. I. Castillo, S. C. Cerda, Generation of bright spatial quasi-solitons by arbitrary initial beam profiles in local and nonlocal (1+1)-dimensional nonlinear media, Optik 202 (2020) 163504 https://doi.org/10.1016/j.ijleo.2019.163504

M. Hesami, M. Avazpour, M. D. I. Castillo, H. Nadgaran, E. Alvarado-Méndez, Observation of a different type of splitting solitons induced by interaction of second order spatial solitons, Optik 245 (2021) 167647 https://doi.org/10.1016/j.ijleo.2021.167647

N. Gürbüz, Intrinsic geometry of the NLS equation and heat system in 3-dimensional Minkowski space, Adv. Studies Theor. Phys. 4 (2010) 557 https://m-hikari.com/astp/astp2010/astp9-12-2010/gurbuzASTP9-12-2010.pdf

M. Ungs, L. P. and A. Gize, The Theory of Quantum Torus Knots: Its Foundation in Differential Geometry- Volume II, (2020) https://books.google.com.tr/books?id= XtuEzQEACAAJ

H. Ceyhan, Z. Özdemir, ˙I. Gök, F. N. Ekmekci, A Geometric Interpretation of Polarized Light and Electromagnetic Curves Along an Optical Fiber with Surface Kinematics, Mediterr. J. Math. 19 (2022) 265. https://doi.org/10.1007/s00009-022-02160-w

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Published

2023-11-01

How to Cite

[1]
S. Nurkan, H. Ceyhan, Z. Özdemir, and İsmail Gök, “Electromagnetic curves and Rytov’s law in the optical fiber with Maxwellian evolution via alternative moving frame”, Rev. Mex. Fís., vol. 69, no. 6 Nov-Dec, pp. 061301 1–, Nov. 2023.

Issue

Vol. 69 No. 6 Nov-Dec (2023): Revista Mexicana de Física

Section

13 Optics

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Copyright (c) 2023 Semra Nurkan, Hazal Ceyhan, Zehra Özdemir, İsmail Gök

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